Goes with my last question. Suppose another line. m, has a slope of 1/2 and -9,2 parallel to m perp to m or neither explain

Question

Please help with this and last

Answer 1

 In short:

 

     Lines are represented by equation of 

 

      Y = mx +b

 

     L1 : Y = m1X + b1

 

     L2:  Y = m2X + b2

 

   L1 & L2 are parallel if and only m1 = m2

 

    L1 & L2 are parallel if and only if m1 = - 1/ m2 , i.e m1 . m2 = -1

 

    In case neither of those 2 conditions are satisfied, then, those 2 lines are neither parallel or    

      perpendicular .

 

       Examples:

 

        Y1 = 5x + 3    Y2 = -1/5 X + 7    Perpendicular.

 

         Y1 = 5x + 3   Y2 = 5X +11       Parallel

 

         Y1 = 2x -11   Y2 = 3x -27       Neither.    

 

 

Answer 2

Hi Mikk;

If the line is parallel, it has the same slope.

If the line is perpendicular, its slope is the negative-inverse.

In your last question, the slope was 1/3.

The parallel line is 1/3.

The perpendicular line is -3/1, -3.

 

has a slope of 1/2 and -9,2

 

I assume that -9,2 is a point...

The equation can be established by using point-slope formula...

y-y₁=m(x-x₁)

y-2=(1/2)(x--9)

Subtracting a negative number is the same as adding a positive number...

y-2=(1/2)(x+9)

y-2=(1/2)x+(9/2)

Let's convert 2 into 4/2...

y-(4/2)=(1/2)x+(9/2)

Let's add 4/2 to both sides...

(4/2)+y-(4/2)=(1/2)x+(9/2)+(4/2)

y=(1/2)x+(13/2)

 

The line parallel to this has a slope of 1/2.

The line perpendicular to this has a slope of -2/1, -2.